How do you make a spiral?
You can easily do this with a Bezier Curve object.

There is a builtin addon shipped by default with Blender that allows drawing spiral objects. You can activate it under the File > User Preferences > Addons > Add Curve: Extra Objects.

Then on the 3D View add a new curve type object, from Add Curve:Spirals > Archemedian

Adjust paremeters to your liking, more importantly Height, Radius and Number of Turns. You can also use Radius Growth although I fear it is insufficient alone.

After creating your base spiral, you can enter Edit Mode in it, activate Proportional Edit , select a buch of spiral loops as desired and use scaling to change the radius into that smooth shape.

Be sure to use S, then Shift+Z to restrict scaling to the XY plane, so it will only make the loops thinner/fatter, without moving them in Z axis.